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mezya [45]
3 years ago
8

The volume of a sphere is increasing at a constant rate of 141 cubic feet per minute. At the instant when the radius of the sphe

re is 11 feet, what is the rate of change of the radius? The volume of a sphere can be found with the equation V=4/3pi r^3 . Round your answer to three decimal places.
Mathematics
1 answer:
ch4aika [34]3 years ago
6 0

Answer:

0.093 ft/min

Step-by-step explanation:

V = 4/3 π r³

Take derivative with respect to time:

dV/dt = 4π r² dr/dt

Plug in values:

141 = 4π (11)² dr/dt

dr/dt = 141 / (484π)

dr/dt ≈ 0.093

The radius is increasing at 0.093 ft/min.

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Can someone explain how to do this
jolli1 [7]

Answer:

20%

Step-by-step explanation:

im not really good at percentages but from what i know you first make it a fraction by adding all the numbers together to get 55(denominator). then for the numerator you take the section that they want(11). 11/55 is equal to 20/100(divide 100 by 55 and multiply the quotient by 11 to get 20). 20/100 is 20%. hope this kinda helps.

7 0
2 years ago
What are all values of x for which the series shown converges? ​
adoni [48]

Answer:

One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:

Iaₙ₊₁I < IaₙI

This means that the absolute value of the terms must decrease as n increases.

Then we must have:

\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}}

We can write this as:

\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}} = \frac{(x -2)^n}{(n + 1)*3^n} * \frac{(x - 2)}{3}

If we assume that n is a really big number, then:

n + 1 ≈ 1

And we can write:

\frac{(x -2)^n}{n*3^n} > \frac{(x -2)^n}{(n)*3^n} * \frac{(x - 2)}{3}

Then we have the inequality

1 > (x - 2)/3

And remember that this must be in absolute value, then we will have that:

-1 < (x - 2)/3 < 1

-3 < x - 2 < 3

-3 + 2 < x < 3 + 2

-1 < x < 5

The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.

5 0
2 years ago
What does x = ? 1 ÷ 11/2 = x
Yanka [14]

Answer:

x = 2/11

Step-by-step explanation:

1 ÷ 11/2 = x

1 · 2/11 = x (Used the opposite reciprocal and changed to multiplication. This is the same as dividing with the original fraction.)

2/11 = x

7 0
3 years ago
Perimeter of a rectangle is 96m. if it's length is 3 times it's width , then find it's length and breadth.​
Stolb23 [73]

Answer:

breadth = 12

length = 36

Step-by-step explanation:

let the breadth be 'x'

length = 3x

p = 2l + 2b

96 = 2(3x) + 2(x)

x = 12

7 0
3 years ago
in chemistry class Andrew has earned scores of 64 69 and 73 on three tests he must maintain an average of 72
olganol [36]
You haven't told me what the question is.  But I put the mouse
to my forehead, closed my eyes, took a deep breath, and I could
see it shimmering in my mind's eye.  It was quite fuzzy, but I think
the question is

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The whole experience drew an incredible amount of energy
out of me, and the mouse is a total wreck.  So we'll just go ahead
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The average score on 4 tests is

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In order for Andrew to have a 72% average on 4 tests,
the sum of the 4 scores must be

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Out of that total that he needs, he already has 

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on the first three tests.

So in order to average 72% for all 4 tests,
he'll need to score

                             (288%  -  206%)  =   82%

on the fourth one.
6 0
3 years ago
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